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3 years ago

Write an equation for the line that passes through (- 3, 5) and is parallel to y = - 6x + 1.

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

3 0

Answer:

y-5 = -6(x+3) OR y = -6x-13

Step-by-step explanation:

Let's use slope-intercept form to solve this problem.

Slope intercept form is the following:

y-y1 = m(x-x1)

x1 and y1 are given by the point in the problem.

x1 = -3, y1 = 5.

m is given by the equation in the problem. Lines that are parallel have the same slope. Thus,

m = -6.

If we plug these values into the equation for slope intercept form, we get the following:

y-5 = -6(x-(-3)) which becomes y-5 = -6(x+3)

This is an acceptable answer to the problem. However, point-slope form is also a way it can be written.

y-5 = -6x-18

y = -6x-13

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What is the value of x? 6x+3= 15

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Read 2 more answers

Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 137.1 ft an

Rama09 [41]

Answer:

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 137.1, \sigma = 3.2$

A tree of this type grows in my backyard, and it stands 132.3 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

This is the pvalue of Z when X = 132.3. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{132.3 - 137.1}{3.2}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

My neighbor also has a tree of this type growing in her backyard, but hers stands 143.5 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.

This is 1 subtracted by the pvalue of Z when X = 143.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{143.5 - 137.1}{3.2}$